It has been found that our preference decision on a visual stimulus is influenced by memory, decision history, and gaze bias. It is generally thought that the stronger the signals of these factors are and the more highly correlated they are to a task, the more influential they are on preference decision. However, here, we report that preference decision is modulated by task-irrelevant motion only when the motion signal is weak. Twenty subjects were asked to choose one of two faces, presented on the left and right of a central fixation point, by moving a joystick to the left or right without eye movements. On each trial during face presentation, a task-irrelevant random dot pattern (moving either leftward or rightward) was presented at one of several coherence levels (0, 5, 10, 20, 50, and 100%). Subjects' choices were significantly biased toward direction of task-irrelevant motion when motion signal was weak (5% coherence), but not higher coherence levels. Following each choice, the subjects were asked to rate their relative preference for the chosen face (“How much do you like the chosen face compared with the other?”) using the joystick on a five-point scale. Subjects' relative preferences were significantly elevated when position of the chosen face corresponded to direction of (5% coherent) task-irrelevant motion. These effects were not observed when task-irrelevant motion moved upward or downward. Another control experiment showed that these effects did not occur when preference decision was made without the lever movement, suggesting that the effects were not simply due to eye movements or attention shifts induced by task-irrelevant motion. On the contrary to the general thought, these results indicate that preference decision on a visual stimulus is gravely influenced by apparently “trivial” signal–the signal that is not only irrelevant to the decision but also extremely weak.